Statistical inference on a flexible loss-based capability index for normal processes

This article introduces a novel process capability index based on a non-symmetric and flexible loss function, designed to enhance the evaluation of manufacturing processes. The proposed index integrates ideas of squared error and absolute error loss functions, providing a versatile framework to capture diverse process deviations while aligning with real-world manufacturing requirements. Beyond its specific application in process capability assessment, the method offers broad applicability in quality control and performance evaluation across various industries. A comprehensive Monte Carlo simulation study is implemented to evaluate the statistical properties of the proposed loss-based capability index, addressing three fundamental inferential problems: (1) point estimation of the loss-based process capability index, (2) construction of confidence intervals for the capability index, and (3) testing the capability on the basis of the non-symmetric loss function. To illustrate its practical implementation, we present a case study from the pipe manufacturing industry, demonstrating how the proposed index effectively addresses real-world challenges such as process capability assessment and quality compliance. The findings highlight the method’s adaptability, making it a valuable tool not only in manufacturing but also in other domains requiring precise deviation analysis and quality assurance.